Iterative Magnetic Resonance Fingerprinting Reconstruction

ABSTRACT

Disclosed herein is a method obtaining a magnetic resonance image of an object, comprising obtaining a first time evolution signal from a magnetic resonance signal from the object; performing a search of a compressed dictionary of magnetic resonance fingerprints to select a magnetic resonance fingerprint representative of the first time evolution signal, wherein the selected magnetic resonance fingerprint is an exact or approximate nearest neighbor match to the first time evolution signal; obtaining a magnetic resonance parameter associated with the selected fingerprint; generating the magnetic resonance image of the object from the obtained magnetic resonance parameter; and performing a second search of the compressed dictionary using the magnetic resonance image.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application Ser.No. 62/245,566, filed Oct. 23, 2015, which is incorporated herein byreference in its entirety.

BACKGROUND OF THE INVENTION

The present disclosure relates generally to magnetic resonancefingerprinting (MRF), and in particular to increase quality of iterativeMRF and to decrease reconstruction time for iterative MRF.

Magnetic resonance fingerprinting is a technique for multi-parametricquantitative imaging. The technique aims to obtain multiple parameters,such as spin-lattice relaxation time (T1) (also known as thelongitudinal relaxation time), spin-spin transverse relaxation time (T2)(also known as the transverse relaxation time), proton density (PD), andthe like, for a test object by applying a series of excitations to atest object, acquiring a signal response of the object to the series ofexcitations, and matching the undersampled signal response to asimulated response found in a dictionary or database of possiblesimulated responses.

Each simulated response stored in the dictionary is generated by runningBloch equations with relevant values for magnetic resonance parameters(T1, T2, PD, and the like). Once a match is found between theundersampled signal response and a simulated response in the dictionary,the magnetic resonance parameters (T1, T2, PD, and the like)corresponding to the matched simulated response can be retrieved fromthe dictionary and used for further imaging purposes. For a singleiteration, the amount of data in an MR signal is not enough to provide amatch to the dictionary entry with sufficient accuracy. Iterativeprocesses are therefore employed to help refine the dictionary matchingprocess. However, iterative processes require the repetition of variouscomputationally expensive steps, such as dictionary search steps andsignal comparison steps.

SUMMARY

Disclosed herein is a method for obtaining a magnetic resonance image ofan object, comprising obtaining a compressed image from one or moremagnetic resonance k-space signals obtained from the object; obtaining afirst time evolution signal from the compressed image; performing asearch of a compressed dictionary of magnetic resonance fingerprints toselect a magnetic resonance fingerprint representative of the first timeevolution signal, wherein the selected magnetic resonance fingerprint isan approximate fingerprint match to the first time evolution signal;obtaining a magnetic resonance parameter associated with the selectedfingerprint; generating the magnetic resonance image of the object fromthe obtained magnetic resonance parameter; and performing a secondsearch of the compressed dictionary using the magnetic resonance image.

Disclosed herein too is a computer program storage medium comprising anon-transitory computer readable medium having program code executableby a processing circuit for implementing a method for forming a magneticresonance image of an object, the program code comprising an instructionto obtain a compressed image form one or more k-space signals obtainedfrom the object; an instruction to obtain a first time evolution signalfrom the compressed image; an instruction to perform a search of acompressed dictionary of magnetic resonance fingerprints to select amagnetic resonance fingerprint representative of the first timeevolution signal, wherein the selected magnetic resonance fingerprint isan approximate fingerprint match to the first time evolution signal; aninstruction to obtain a magnetic resonance parameter associated with theselected fingerprint; an instruction to generate the magnetic resonanceimage of the object from the obtained magnetic resonance parameter; andan instruction to perform a second search of the compressed dictionaryusing the magnetic resonance image.

Disclosed herein too is an apparatus for obtaining a magnetic resonanceimage of an object, comprising a magnetic resonance device for obtainingone or more magnetic resonance k-space signals from the object; and aprocessor configured to: obtain a compressed image from the one or morek-space signals; obtain a first time evolution signal from thecompressed image; perform a search of a compressed dictionary ofmagnetic resonance fingerprints to select a magnetic resonancefingerprint representative of the first time evolution signal, whereinthe selected magnetic resonance fingerprint is an approximatefingerprint match to the first time evolution signal; obtain a magneticresonance parameter associated with the selected fingerprint; generatethe magnetic resonance image of the object from the obtained magneticresonance parameter; and perform a second search of the compresseddictionary using the magnetic resonance image.

The above features and advantages and other features and advantages ofthe invention are readily apparent from the following detaileddescription of the invention when taken in connection with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring to the exemplary non-limiting drawings wherein like elementsare numbered alike in the accompanying Figures:

FIG. 1 illustrates a method of magnetic resonance fingerprinting (MRF)in one embodiment;

FIG. 2 shows various images based on parameters retrieved from afingerprint dictionary using the method disclosed herein;

FIG. 3 shows a schematic diagram of an iterative method forreconstructing an image using MRF;

FIG. 4 schematically illustrates an effect of singular valuedecomposition in compressing a fingerprint dictionary.

FIG. 5 shows a method of k-d tree construction for a search space;

FIG. 6 illustrates a search method for selecting data points in thesearch space of FIG. 5 using k-d tree branching method; and

FIG. 7 shows a schematic diagram of an apparatus for providing amagnetic resonance image of an object in one embodiment.

DETAILED DESCRIPTION OF THE INVENTION

Although the following detailed description contains many specifics forthe purposes of illustration, anyone of ordinary skill in the art willappreciate that many variations and alterations to the following detailsare within the scope of the claims. Accordingly, the following exampleembodiments are set forth without any loss of generality to, and withoutimposing limitations upon, the claimed invention.

Disclosed herein is a method for imaging an object using acceleratediterative reconstruction for magnetic resonance fingerprinting (AIR-MRF)methods. The object is generally tissue from a living being. The methodcomprises obtaining a time evolution signal from a magnetic resonancesignal of the object and performing a search of a compressed dictionaryof magnetic resonance fingerprints to select a magnetic resonancefingerprint representative of the time evolution signal. In anembodiment, the selected magnetic resonance fingerprint is a nearestneighbor match to the time evolution signal. Magnetic resonanceparameters associated with the selected fingerprint are obtained. Amagnetic resonance image of the object is generated from the obtainedmagnetic resonance parameter.

Magnetic resonance fingerprinting (MRF) is a process for determiningrelevant magnetic resonance parameters of an object by matching amagnetic resonance response signal obtained from an experiment or testperformed on the object to a magnetic resonance response signal storedin a database. In its simplest form, MRF is analogous to matching aperson's real fingerprint to a database of fingerprints. Once a matchbetween a fingerprint sample and a fingerprint stored in a database hasbeen made, a host of additional information about the person such asname, address and phone number can be obtained. In MRF,experimentally-acquired magnetic resonance imaging data is compared tosimulated magnetic resonance imaging data (also referred to herein as a“fingerprint”) stored in a fingerprint database or fingerprintdictionary. Once a match is made, various magnetic resonance parameterscan be retrieved from the dictionary, including spin-lattice relaxationtime (T1), spin-spin relaxation time (T2), off-resonance frequency,proton density (PD), perfusion, and magnetization transfer (MT) as wellas other magnetic resonance parameters. Magnetic resonance images can begenerated using the selected magnetic resonance parameters.

In one embodiment, the experimentally-acquired magnetic resonanceimaging data is a time evolution signal and the fingerprints stored inthe dictionary are simulated time evolution signals. The simulated timeevolution signals are created by applying the Bloch equation formagnetic resonance to all foreseeable combinations of magnetic resonanceparameters such as, for example, the magnetic parameters listed above(T₁, T₂, off-resonance frequency, proton density, perfusion,magnetization transfer). A dictionary entry includes the fingerprint(i.e., the simulated time evolution signal) as well as the correspondingmagnetic resonance parameters used in the Bloch equation to produce thefingerprint. Once this dictionary of fingerprints has been generated, amatching algorithm can be used to find a fingerprint that best orsuitably matches the acquired time evolution signal. The magneticresonance parameters associated with the matched fingerprint can then beretrieved from the dictionary.

FIG. 1 illustrates a method of magnetic resonance fingerprinting (MRF)in one embodiment. A magnetic resonance (MR) k-space signal 102 isobtained using a pseudorandom excitation signal to excite the nuclei ofthe object being tested. The pseudorandom excitation signal includes aplurality of rotation pulses characterized by various acquisitionparameters such as flip angle (FA), phase of RF pulses, repetition time(TR), echo time (TE), and the like. These acquisition parameters arevaried during data collection in a pseudorandom manner. Each pulserotation of the excitation signal causes the nuclei to produce a signal102 that takes the form of a spiral in k-space. The excitation signalincludes a plurality of rotation pulses, leading to the creation of aplurality of spiral signals 102. In the embodiments discussed herein,the number of rotation pulses can vary from 50 to 1000. However, this isnot meant to limit the invention. Each spiral signal 102 can be used tocreate an image 104 of the object via a Fourier transform. Thus, animage 104 is created for each rotation pulse of the excitation signal.Image 104 is generally of a poor quality due to signal undersampling.However, the information within the plurality of images 104 can be usedto select fingerprints from a fingerprint dictionary, as is detailedbelow.

The images 104 can be two-dimensional or three-dimensional images, invarious embodiments. A time evolution signal can be formed using signalsselected from a same pixel or voxel position of each of the plurality ofimages, for example, the voxel at the lower left corner of each of theplurality of images. The time evolution signal for the selected voxelposition is compared to fingerprints stored in the dictionary in orderto determine magnetic resonance parameters associated with the selectedvoxel position.

Graph 106 shows a time evolution signal 108 obtained from experiment aswell as a simulated time evolution signal or fingerprint 110 selectedfrom a fingerprint dictionary. While the time evolution signal 108displays various spikes and other noise features, the fingerprint 110 isdevoid of such noise. A search method discussed below is used to comparethe fingerprint 110 to the time evolution signal 108 to determinewhether the fingerprint is a suitable match for the time evolutionsignal 108. Once a selected fit is determined between time evolutionsignal 108 and fingerprint 110, the magnetic resonance parameters (e.g.,T1, T2, PD, and the like) associated with the matched fingerprint can beretrieved from the dictionary.

This matching process is performed for substantially all voxels in thesequence of images in order to retrieve MR parameters for each voxel.Once this process has been performed for all voxel positions for aselected MR parameter, the voxels can be combined to create an image forthe selected MR parameter. FIG. 2 shows various images based onretrieved MR parameters. Image 201 is based on the T1 parameter. Image205 is based on the T2 parameter. Image 203 is based on theoff-resonance frequency. Image 207 is based on the spin density (M₀).

FIG. 3 shows a schematic diagram 300 of an iterative method forreconstructing an image using MRF, referred to herein as acceleratediterative reconstruction for magnetic resonance fingerprinting(AIR-MRF). The method includes a data fidelity stage 302 and a signalmatching stage 304. In the data fidelity stage 302, an MR k-space signalis prepared to provide data for a dictionary search that occurs in thesignal matching stage 304. Each iteration of the method provides aresult from the signal matching stage 304 for input to the data fidelitystage 302 for the next iteration. Through iteration, the MR k-spacesignal can be used to update or modify an image previously generated atthe signal matching stage 304.

In a first iteration, one or more undersampled k-space signals arereceived at box 306, the undersampled k-space signals being separatedtemporally. At box 308, the undersampled k-space signals 306 arecompressed and an inverse Fourier transform is performed in order toobtain one or more images in a compressed space from the one or moreundersampled k-space signals 306. The one or more compressed images canbe stored at a memory location and can be retrieved during subsequentiterations. Continuing through the data fidelity stage 302, the one ormore images in the compressed space are provided to a differencegenerator 318 that determines a difference between the one or morecompressed images and one or more compressed images from a previousiteration. Since this is the first iteration, the “previous” one or morecompressed images can be a null images or images that are initialized toinclude non-zero values, such as a temporal average of image values. Theone or more compressed images created at the difference generator 316are scaled by a factor or “step size” a at scaling box 320. The scaledone or more images are then used to update the one or more images fromthe previous iteration at a summing device 322. The one or more updatedimages are then provided to the signal matching stage 304.

For second and subsequent iterations, one or more compressed images 310created during the signal matching stage 304 during a previous iterationare output from the signal matching stage 304 and are provided as inputto the data fidelity stage 302. In box 312, the previous one or morecompressed images 310 undergo a Fourier transform to obtain k-space dataand the resulting k-space data is decompressed. In box 314, a samplingmask is applied to the decompressed k-space data. The sampling maskcreates an undersampled data set in k-space which is compared (at box330) to the measured undersampled k-space signals from box 306 in orderto determine a scalar difference between them. This scalar difference isused to determine the step size a for box 320. This scaling can beapplied once at the second iteration or every time for the subsequentiterations. In box 316, the undersampled data from box 314 is compressedand a Fourier transform is performed in order to obtain one or morecompressed images. Imaging issues that occur due to multichannel coilsensitivities that occur during MR data acquisition can be resolved atthese stages. In one embodiment, the resolution of such imaging issuesoccurs during the Fourier transform. At difference generator 318, theone or more compressed images from box 316 are subtracted from the oneor more compressed images from box 308 in order to generate an imagegradient. In one embodiment, the one or more compressed images from box308 are images that were stored in a memory location or memory storagedevice during the first iteration. Thus, there is no need during thesecond and subsequent iterations to once again perform the steps ofboxes 306 and 308, although one can perform these steps in alternateembodiments. In box 320, the image gradient is scaled by the determinedstep size a. The scaled image gradient and the one or more previousimages 310 are supplied to summing device 322. Summing device 322 addsthe scaled imaged gradient to the one or more previous images 310 toobtain one or more updated images. The one or more updated images arethen supplied from the summing device 322 to the signal matching stage304.

For all iterations, the signal matching stage 304 receives the one ormore updated images from the data fidelity stage 302, determines a timeevolution signal for the one or more images and performs a dictionarysearch to locate a fingerprint that is an acceptable match to the timeevolution signal. Since the one or more updated images received at thesignal matching stage 304 are compressed images, the time evolutionsignal obtained from the one or more images is a compressed timeevolution signal that is not necessarily temporally consistent. However,it is possible to construct a temporally-consistent time evolutionsignal from the compressed time evolution signal. Once a fingerprint hasbeen selected, the magnetic resonance parameters 326 associated with thefingerprints can be retrieved from the dictionary. The retrievedparameters 326 can be used to generate one or more compressed images310. In various embodiments, the one or more compressed images 310 canbe further modified by a regularization step (box 328). In oneembodiment of the regularization step (box 328), an image is generatedusing one or more of the MR parameters 326 retrieved from the databaseand the image is multiplied by an associated fingerprint in order tomodify the compressed images 310. The generated compressed images 310are provided as input to the data fidelity stage 302. The retrievedparameters 326 can be stored at a memory location or memory storagedevice and used in subsequent iterations of the signal matching stage304 to facilitate a subsequent search of the dictionary.

The dictionary search of the signal matching stage 304 includes a stepfor comparing data and a searching algorithm that determines how tonavigate through the dictionary efficiently to locate an optimal ornearest neighbor fingerprint for the time evolution signal. Both thecomparison step and the search step can be computationally expensive.

In one aspect, the method disclosed herein reduces computation time forcomparing data by compressing dictionary entry data to obtain arepresentation of the dictionary entry in a more compact space. Variouscompression methods may include a singular value decomposition (SVD) orprincipal component analysis (PCA). In one embodiment, singular valuedecomposition (SVD) is used on the dictionary fingerprints in order toreduce the computation time for matching experimentally-acquired timeevolution signals to fingerprints and for performing the various Fouriertransforms of the data fidelity stage 302 and the signal matching stage304. SVD can be performed on the dictionary fingerprints prior toobtaining any MR k-space signals.

In order to determine a quality of fit between a time evolution signaland a fingerprint, an inner product is performed to obtain a valuek_(i), the inner product taking the form of Eq. (1):

$\begin{matrix}{{\hat{k}}_{i} = {\underset{k_{j}}{\arg \; \max}\frac{{Re}{\langle{D_{j},X_{i}}\rangle}}{{D_{j}}^{2}}}} & {{Eq}.\mspace{14mu} (1)}\end{matrix}$

where D_(j) is the j^(th) dictionary fingerprint and X_(i) is the timeevolution signal. Comparing the values of {circumflex over (k)}_(j) formultiple dictionary entries allows one to locate a fingerprint {umlautover (k)}_(i) that is an acceptable fit to the time evolution signal.Mathematically, the dictionary D can be denoted by Dε

^(nxt) where n is the number parameter combinations and t is the numberof time points. The j^(th) entry (or j^(th) fingerprint) is denoted byD_(j) wherein j=1, . . . , n. For an observed time evolution signal, itsdictionary match is determined by Eq. (1) above.

Every matrix Aε

^(pxq) can be written using SVD such that

A=UΣV*   Eq. (2)

where Uε

^(pxp) and Vε

^(qxq) are unitary matrices, and ΣεR^(pxq) is a diagonal matrixcontaining the non-increasing singular values σ_(i, i=)1, . . . ,min{p,q}. The columns of U are denoted u₁, . . . , u_(p) and are calledthe left singular vectors. The columns of V are denoted v₁, . . . ,v_(q) and are called the right singular vectors.

Since Dε

^(pxq), SVD can be applied to the dictionary D of fingerprints as shownin Eq. (3):

D=UΣV*   Eq. (3)

where U, V, and Σ are as described above. For a given index j (1≦j≦r,where r=rank(D)), a truncated SVD can be written in matrix form to yielda low-rank approximation of the dictionary:

D≈U_(j)Σ_(j)V_(j)*   Eq. (4)

where U_(k)=[u₁, . . . , u_(j)] denotes the matrix containing the firstj left singular vectors and similar matrices are formed for Σ_(j) andV_(j).

The first j right singular vectors {v₁, . . . , v_(j)} form anorthonormal basis for the rows of D. Therefore each dictionary entryD_(j) can be written as a linear combination of these orthogonalvectors. By projecting the dictionary onto the subspace spanned by thefirst j right singular vectors {v₁, . . . , v_(j)}, the dictionary isreduced to a compressed dictionary in a lower-dimensional space

^(k) that can be written as

D_(j)=DV_(j)  Eq. (5)

Meanwhile, the time evolution signal X_(j) can be projected onto thesame subspace spanned by the vectors in V_(j) by

X_(j)=XV_(j)  Eq. (6)

The compressed dictionary D_(j) and the SVD of the signal X_(j) can beused in Eq. (1) to reduce computation time and cost for fingerprintselection, as discussed below with respect to FIG. 4.

FIG. 4 schematically illustrates an effect of singular valuedecomposition on the dictionary. The size of uncompressed dictionary 402is indicated by the number of entries in the dictionary 402 and thelength of the pulse sequence. The size of compressed dictionary 404 isindicated by the number of entries in the compressed dictionary 404 anda compressed length. The number of entries in the compressed dictionary404 is the same as the number of entries in the uncompressed dictionary402. However, the length of each entry in the compressed dictionary 404is less than the length of each entry in the uncompressed dictionary402. This reduced length subsequently reduces the computation time andcost for performing the calculation of Eq. (1).

In another aspect, the method disclosed herein reduces computation timeand energy spent on a searching algorithm by allowing the selection ofan approximate nearest-neighbor entry rather than an optimalfingerprint. Due to the large number of dictionary entries, a searchalgorithm is employed to increase the efficiency in locating an optimalor near-optimal fingerprint from the dictionary. An exemplary searchalgorithm includes a k-d tree search algorithm that includes defining ak-d tree over the dictionary space and performing a search using the k-dtree. The k-d tree is a binary tree in which every node is ak-dimensional point. The k-d tree begins at a root node, which indicatesan entire search space and includes multiple nodes which facilitate thesearch process. A branch of the k-d tree ends in a leaf, indicating adictionary entry or fingerprint. Every non-leaf node can be thought ofas implicitly generating a splitting hyperplane that divides the searchspace into two parts, known as half-spaces. In other words, the searchspace of the dictionary is separated by a number of binary spacepartitions, as discussed with respect to FIG. 5.

FIG. 5 shows a method of k-d tree construction for a search space with asimplified two-dimensional example (k=2). The search space represents anentire search space of the dictionary. The search space is representedby the large rectangle 501 and is occupied by dictionary entries,represented by data points 1 through 22. The search space 501 ispartitioned by plane 503 into a left half-space 502 including datapoints 1 through 10 and a right half-space 504 including data points 11through 22. The left half-space 502 is further partitioned into twosmaller spaces by plane 505, one of which includes data points 1-5 andthe other of which includes data points 6-10. Similarly, the righthalf-space is further divided into two smaller spaces by plane 507, oneof which includes data points 11-16 and the other of which includes datapoints 17-22. This method of binary partitioning of spaces can becontinued any number of times, including until each data point residesuniquely in its own search space.

FIG. 6 shows a search method for selecting data points shown in FIG. 5using the k-d tree branching method. Node 601 is a root noderepresenting a search over the entire search space 501. Node 602represents left half-space 502 and node 604 represents right half-space504.

An operation is performed at node 601 to decide which of the searchspaces (502, 504) to select. The operation provides values for acomparison between a time evolution signal and a representative timeevolution signal of the left half-space 502 as well as for between thetime evolution signal and a representative time evolution signal of theright half-space 504. A comparison of these values determines whether tocontinue the search in the left half-space 502 (node 602) or the righthalf-space 504 (node 604). At each node, another set of operations andcomparisons is made to determine which of the next lowest nodes tosearch. In a first part of the search, this process continues until aleaf is has been located. Once the leaf has been located, nearby leavesare evaluated in order to determine an optimal match. Referring to FIG.5, a query point 510 representing a time evolution signal is shownresiding in a search space for data point ‘5’. However, it is possiblethat another data point (such as data point ‘3’) provides a closermatch. Therefore, in a second part of the search, a hypersphere 512 isdrawn about the query point 510 with radius defined by the pointinitially selected from the first part of the search (i.e., leaf ‘5’),and data points in spaces intersecting with this hypersphere 512 arechecked to determine an improved or optimal match with the timeevolution signal. In one aspect of the present invention, the secondpart of the search is limited in extent so that only a selected numberof the data points within the hypersphere 512 are checked during anygiven iteration of the AIR-MRF shown in FIG. 3. During subsequentiterations of AIR-MRF, the first part of the search can be performedwith a new query point to locate a new leaf and a new hypersphere can bedefined with respect to the new query point for the second part of thesearch. The radius of the new hypersphere can be a minimum of thedistance between the new query and the new leaf located during the firstpart of the search and the distance between the new query and the leaflocated during the previous first stage. The new hypersphere can be usedto immediately eliminate some candidate points, thus improving searchresults and/or reducing search time. In one embodiment, when the querypoint during one iteration does not change much from the query point inthe previous iteration, it is possible to skip the first part of searchfor subsequent iterations in order to speed up the search process.However, maintaining the first part of the search provides aninsignificant time penalty, even if the query point changessignificantly. Meanwhile, removing the first stage can degrade searchresults for when the query point changes significantly.

In one embodiment, a fingerprint dictionary is compressed using singularvalue decomposition, and the search algorithm is performed usingcompressed fingerprints of the compressed dictionary when searchingthrough the dictionary. The search algorithm used in navigating thedictionary includes the k-d tree search discussed above. The searchalgorithm can be stopped before an optimal fingerprint is selected fromthe database. The fingerprint found during this truncated search istherefore an approximate fingerprint to an optimal fingerprint selectionrather than the optimal fingerprint selection itself

Computation time is therefore reduced both by using the compresseddictionary and by modifying the search algorithm to accept approximatefingerprints rather than optimal fingerprints. Fourier transform timesare further reduced by use of SVD compression, since the linearity ofthe compression allows the Fourier operations to be performed on areduced set of compressed data.

The approximate fingerprint can be used in subsequent iterations of theAIR-MRF shown in FIG. 3. In other words, once the approximatefingerprint is selected, magnetic resonance parameters (i.e., T1, T2,PD, and the like) associated with the approximate fingerprint areselected from the compressed dictionary to form compressed images. Thecompressed images are then input to the data fidelity stage 302 of FIG.3.

While the parameters obtained for an approximate fingerprint can bedifferent than the parameters obtained for an optimal fingerprint, theiterative process of FIG. 3 is stable to such differences. Forsubsequent iterations the search algorithm can search for betterapproximate fingerprints.

While an exhaustive search would require checking all possible matcheswithin this hypersphere 512, which in some cases could involve searchingevery single leaf node in the tree, the truncated search disclosedherein for selecting approximate fingerprints reduces search time bychecking only a fixed number of leaf nodes within the hypersphere 512for any one iteration. The best match after a limited number of leafnode checks is considered the approximate match to the time evolutionsignal. In one embodiment, the selected number of the data points tocheck can vary with each iteration.

The number of data points to check can be different with each iterationto adjust for quality and performance.

During iterative MRF reconstruction, we can assume that the parameterestimates for a given voxel will not typically change drastically fromone iteration to the next. Thus, for the second and subsequentiterations, the approximate fingerprint selected during the previousiteration is used as an initial guess for the closest dictionary match.This eliminates data points of the k-d tree that do not contain closermatches. By incorporating this prior information, the search process isaccelerated beyond what can be obtained using conventional k-d treesearches.

FIG. 7 shows a schematic diagram of an apparatus 700 for providing amagnetic resonance image of an object in one embodiment. The object isplaced in the MRI device 702 which applies the excitation pulse havingacquisition parameters that are varied in a pseudorandom manner. Thedata from the MRI device 702 is sent to processor 704 which performs theAIR-MRF process shown in FIG. 3. The processor 704 also produces acompressed fingerprint dictionary and performs the nearest neighborsearch on the compressed dictionary. In various embodiments, thecompressed fingerprint dictionary is computed prior to the iterativemethods disclosed in FIG. 3 and is stored in a memory location or memorystorage device so as to be accessible to processor 704. Images formed bythe processor can be shown at monitor/display 706 for review by atechnician or medical personnel perform a diagnosis on the object.

In view of the foregoing, it will be appreciated that an embodiment maybe embodied in the form of computer-implemented processes andapparatuses for practicing those processes. An embodiment may also beembodied in the form of a computer program product having computerprogram code containing instructions embodied in tangible media, such asfloppy diskettes, CD-ROMs, hard drives, USB (universal serial bus)drives, or any other computer readable storage medium, such as randomaccess memory (RAM), read only memory (ROM), erasable programmable readonly memory (EPROM), electrically erasable programmable read only memory(EEPROM), or flash memory, for example, wherein, when the computerprogram code is loaded into and executed by a computer, the computerbecomes an apparatus for practicing the invention. An embodiment mayalso be embodied in the form of computer program code, for example,whether stored in a storage medium, loaded into and/or executed by acomputer, or transmitted over some transmission medium, such as overelectrical wiring or cabling, through fiber optics, or viaelectromagnetic radiation, wherein when the computer program code isloaded into and executed by a computer, the computer becomes anapparatus for practicing the invention. When implemented on ageneral-purpose microprocessor, the computer program code segmentsconfigure the microprocessor to create specific logic circuits.

While the invention has been described with reference to exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the claims. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the invention without departing from theessential scope thereof. Therefore, it is intended that the inventionnot be limited to the particular embodiment disclosed as the best oronly mode contemplated for carrying out this invention, but that theinvention will include all embodiments falling within the scope of theappended claims. Also, in the drawings and the description, there havebeen disclosed example embodiments and, although specific terms may havebeen employed, they are unless otherwise stated used in a generic anddescriptive sense only and not for purposes of limitation, the scope ofthe claims therefore not being so limited. Moreover, the use of theterms first, second, and the like do not denote any order or importance,but rather the terms first, second, and the like are used to distinguishone element from another. Furthermore, the use of the terms a, an, andthe like do not denote a limitation of quantity, but rather denote thepresence of at least one of the referenced item.

Additionally, the term “comprising” as used herein does not exclude thepossible inclusion of one or more additional features.

What is claimed is:
 1. A method for obtaining a magnetic resonance image of an object, comprising: obtaining a compressed image from one or more magnetic resonance k-space signals obtained from the object; obtaining a first time evolution signal from the compressed image; performing a first search of a compressed dictionary of magnetic resonance fingerprints to select a magnetic resonance fingerprint representative of the time evolution signal, wherein the selected magnetic resonance fingerprint is an approximate fingerprint match to the first time evolution signal; obtaining a magnetic resonance parameter associated with the selected fingerprint; generating the magnetic resonance image of the object from the obtained magnetic resonance parameter; and performing a second search of the compressed dictionary using the magnetic resonance image.
 2. The method of claim 1, wherein an entry of the compressed dictionary includes a singular value decomposition of a fingerprint.
 3. The method of claim 2, wherein selecting the representative magnetic resonance fingerprint further comprises comparing a singular value decomposition of the first time evolution signal to the singular value decomposition of the fingerprint.
 4. The method of claim 3, further comprising calculating a distance using the singular value decomposition of the first time evolution signal and the singular value decomposition of the fingerprint.
 5. The method of claim 1 wherein the obtained magnetic resonance parameters include at least one of (i) a spin-lattice relaxation; (ii) a spin-spin relaxation; (iii) a proton density; (iv) a spin density; and (v) an off-resonance frequency.
 6. The method of claim 1, wherein performing the first search further comprises performing a k-d tree search of the compressed dictionary through to select a leaf node of the k-d tree and performing a search of a selected number of data points within a hypersphere of the selected leaf node to select the approximate fingerprint.
 7. The method of claim 6, wherein performing the second search of data points to select a new approximate fingerprint from within a hypersphere defined by the approximate fingerprint selected during the first search.
 8. The method of claim 1, further comprising applying a regularization step to the magnetic resonance image and enforcing data fidelity on the regularized magnetic resonance image by compensating for a difference between the regularized magnetic resonance image and acquired data.
 9. The method of claim 1, further comprising generating a second time evolution signal from the generated magnetic resonance image and a fingerprint associated with the magnetic resonance image and performing the second search of the compressed dictionary using the second time evolution signal.
 10. A computer program storage medium comprising a non-transitory computer readable medium having program code executable by a processing circuit for implementing a method for forming a magnetic resonance image of an object, the program code comprising: an instruction to obtain a compressed image form one or more k-space signals obtained from the object; an instruction to obtain a first time evolution signal from the compressed image; an instruction to perform a first search of a compressed dictionary of magnetic resonance fingerprints to select a magnetic resonance fingerprint representative of the time evolution signal, wherein the selected magnetic resonance fingerprint is an approximate fingerprint match to the first time evolution signal; an instruction to obtain a magnetic resonance parameter associated with the selected fingerprint; an instruction to generate the magnetic resonance image of the object from the obtained magnetic resonance parameter; and an instruction to perform a second search of the compressed dictionary using the magnetic resonance image.
 11. The computer program storage medium of claim 10, further comprising an instruction to form an entry of the compressed dictionary by performing a singular value decomposition on a fingerprint.
 12. The computer program storage medium of claim 11, wherein selecting the representative magnetic resonance fingerprint further comprises comparing a singular value decomposition of the first time evolution signal to the singular value decomposition of the fingerprint.
 13. The computer program storage medium of claim 12, further comprising an instruction to determine a distance using the singular value decomposition of the first time evolution signal and the singular value decomposition of the fingerprint.
 14. The computer program storage medium of claim 10, wherein the obtained magnetic resonance parameters include at least one of (i) a spin-lattice relaxation; (ii) a spin-spin relaxation; (iii) a proton density; (iv) a spin density; and (v) an off-resonance frequency.
 15. The computer program storage medium of claim 10, wherein performing the first search further comprises performing a k-d tree search of the compressed dictionary to select a leaf node of the k-d tree and performing a search of a selected number of data points within a hypersphere of the selected leaf node to select the approximate fingerprint.
 16. The computer program storage medium of claim 15, wherein performing the second search of data points further comprises selecting a new approximate fingerprint from within a hypersphere defined by the approximate fingerprint selected during the first search.
 17. The computer program storage medium of claim 10, further comprising an instruction to apply a regularization step to the magnetic resonance image and enforce data fidelity on the regularized magnetic resonance image by compensating for a difference between the regularized magnetic resonance image and acquired data.
 18. The computer program storage medium of claim 10, further comprising an instruction to generate a second time evolution signal from the generated magnetic resonance image and a fingerprint associated with the magnetic resonance image and perform the second search of the compressed dictionary using the second time evolution signal.
 19. An apparatus for obtaining a magnetic resonance image of an object, comprising: a magnetic resonance device for obtaining one or more magnetic resonance k-space signals from the object; and a processor configured to: obtain a compressed image from the one or more k-space signals; obtain a first time evolution signal from the compressed image; perform a search of a compressed dictionary of magnetic resonance fingerprints to select a magnetic resonance fingerprint representative of the first time evolution signal, wherein the selected magnetic resonance fingerprint is an approximate fingerprint match to the first time evolution signal; obtain a magnetic resonance parameter associated with the selected fingerprint; generate the magnetic resonance image of the object from the obtained magnetic resonance parameter; and perform a second search of the compressed dictionary using the magnetic resonance signal.
 20. The apparatus of claim 19, wherein the magnetic resonance device is configured to excite nuclei of the object using an excitation signal having parameters that are varied in a pseudorandom manner.
 21. The apparatus of claim 19, wherein selecting the representative magnetic resonance fingerprint further comprises comparing a singular value decomposition of the first time evolution signal to a singular value decomposition of the fingerprint.
 22. The apparatus of claim 19, wherein the processor performs the first search by performing a k-d tree search of the compressed dictionary to select a leaf node of the k-d tree and performing a search of a selected number of data points within a hypersphere of the selected leaf node to select the approximate fingerprint.
 23. The apparatus of claim 19, wherein the processor applies a regularization step to the magnetic resonance image and enforces data fidelity on the regularized magnetic resonance image by compensating for a difference between the regularized magnetic resonance image and acquired data.
 24. The apparatus of claim 19, wherein the processor generates a second time evolution signal from the generated magnetic resonance image and a fingerprint associated with the magnetic resonance image and performs the second search of the compressed dictionary using the second time evolution signal. 